判定局部共形Khler流形为Vaisman流形的若干定理  

Several judging theorems of Vaisman manifold about locally conformally Khler manifold

作　　者：杨永举[1] 王学强[1] 

机构地区：[1]南阳师范学院数学与统计学院,河南南阳473061

出　　处：《南阳师范学院学报》2013年第6期5-7,共3页Journal of Nanyang Normal University

基　　金：河南省基础与前沿技术研究计划项目(112300410300);南阳师范学院专项项目(nytc2005k37);南阳师范学院校级教改项目

摘　　要：利用覆盖映射和局部共形Khler流形理论,证明了满足某些条件的局部共形Khler流形一定为Vaisman流形的若干定理.如:Lee向量场为一个群S(eit,t∈R)作用诱导下的向量场一定为Vaisman流形.同时文中也给出判断Vaisman流形的若干充要条件.By applications of theories of locally conformally Kāihler manifold and universal covering theorems , the following several results are proved in this paper. Some kind of locally conformal compact manifold must be Vaisman manifold,for example, a locally conformal compact Kāhler manifold with Lee vector field induced by group S（e^it,t∈R） must be Vaisman manifold, and that several special methods are given, which is sufficient and necessarily to judge Vaisman manifold.

关 键 词：局部共形Kahler流形 Vaisman流形 Lee形式 

分 类 号：O174.56[理学—数学]